There are a bunch of different practical implementations, as per https://crdt.tech/implementations https://crdt.tech/implementations https://www.antidotedb.eu

There are a bunch of different practical implementations, as per https://crdt.tech/implementations https://crdt.tech/implementations https://www.antidotedb.eu https://www.antidotedb.eu is an example of a CRDT database that very much hits disk and preserves the mathematical guarantees. It's based on transactional causal+ consistency, which is formally proven to be the strongest consistency mode for an AP database. Other great examples are https://automerge.org https://automerge.org and https://www.macrometa.com https://www.macrometa.com (Disclaimer: building a database system on top of Antidote at https://vaxine.io https://vaxine.io).